36 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. J I 



Between i.oo day and 2.58 days, the frequencies were counted for 

 each o.oi day ; between 2.58 days and 4.16, for each 0.02 day ; between 

 4.16 and 10.60, for 0.04 day ; between 10.16 and 18.20, for o.-io day ; 

 between 18.20 and 34.00 for 0.20 day, and between 34 and 74 days, 

 for 0.50 day. The results were smoothed by taking successive over- 

 lapping sums of five and these results are shown in figures 11 and 12. 

 The frequencies are greater for the shorter periods because of the 

 greater possibility of occurrence, but no correction was attempted. 



The count of the frequencies and the plot were made by Mr. 

 William Hoxmark. In the plot the ordinates are frequencies and 

 the abscissas are length of periods. 



The periods indicated by maximum frequencies are given in table 

 XIII, in which the periods most strongly indicated are designated by 

 an asterisk. 



Turning to the periods exceeding 26 days, it is seen that periods are 

 indicated at about 26, 28, 30, 32, 36, 40, and 54 days. 



The shorter periods appear to be submultiples of these longer 

 periods as shown in table XIV. In this table, 44 days was substi- 

 tuted for 54 as the submultiples of this period appeared to be stronger 

 than that of 54. 



The next step was to ascertain if there was sufficient permanency 

 to the periods to form mean values for a considerable length of time. 

 To do this, it is only necessary to take means of successive values of 

 2/r cos 9 and of 2/,- sin 6 for as many successive periods as desired 

 and then compute and a from the mean values. 



Overlapping means were obtained for 3, for 9 and for 18 periods. 

 The results showed periods of nearly the same lengths as the indi- 

 vidual periods and gave the lengths with greater accuracy (see 

 figures 13 and 14), the length of the periods above 20 days being 

 indicated as 22.0, 26.4, and 30.8 (see table XIII). 



As a further test, the calculations for the 30-day period were 

 extended backward to 191 1 for successive means of nine periods. 

 The interval taken for the calculations was one-twelfth of a year and 

 the computed azimuths and amplitudes are plotted in figure 15. From 

 191 1 to 1915 a line connecting the plotted azimuths slants upward 

 indicating a period of 30.1 days. At the beginning of 191 5 a sudden 

 change in the slope of the line indicates a period between 33 and 34 

 days during 1915 and of about 31.2 days during 1917 and 1918. 



This change of length is curiously related with solar activity, there 

 being a sun-spot minimum from 191 1 to 1914 and a greatly increased 

 solar activity beginning with 191 5. 



